Note: I haven't watched the whole series yet.
A glance at the cover art is sufficient proof that this is not a typical anime series.
The director uses a perfect relational metaphor for the series. When you first meet somebody, you know nothing about him or her. But as you ask questions and see how the person reacts, you learn basic attributes—interests, hobbies, likes, dislkes—then you discover dreams and fears, and eventually you really know the person. That's Mushi-shi; slow, gradual discovery.
The show is entirely episodic. One man appears in every episode: Ginko, a Mushi-shi, or Mushi master. In this world, Mushi are primordial life-forms pervading the world (much like The Force, despite "mushi" being the Japanese word for normal insects). Some people see the Mushi in their many forms, and the interactions between people and Mushi can be dangerous.
So, each episode follows the same pattern: A remote village or person suffers from some problem or strange situation. Ginko arrives, uncovers the Mushi-related reason, and figures out a way to deal with it.
But this series diverges from typical storytelling in its dealing with that last bit. Usually, the Mushi are involved because humans' reach exceeds their grasp. People want something...unusual. Sometimes their motivations are selfish; sometimes pure. The heartbreaking stories involve those with honorable, self-sacrificing intentions who nevertheless ensnare themselves and others in cycles of pain.
The series is fascinating because each episode is a morality tale. But there's no clear moral. It's an investigation of morality. Each episode holds up a person's moral outlook, like a crystal, so the viewer can examine its many facets. And we can observe the consequences. The show coquettishly avoids giving us any black-or-white conclusions.
In a typically Asian way, good is often not explicitly rewarded, nor is selfishness always punished. This is, after all, the story of strange primoridal creatures with no concept of morality. But characters must make moral choices, and live with the consequences.
Like us.